On the Structure of Some Reduced Amalgamated Free Product C*-Algebras

TL;DR

This paper investigates the structure of certain reduced amalgamated free product C*-algebras, providing conditions for their positive cone, simplicity, and trace uniqueness, with applications to Baumslag-Solitar groups.

Contribution

It offers new criteria for the positive cone, simplicity, and trace uniqueness in reduced free product C*-algebras, including a complete characterization for Baumslag-Solitar groups.

Findings

Conditions for the positive cone to be maximal

Criteria for simplicity and trace uniqueness

Characterization for Baumslag-Solitar group C*-algebras

Abstract

We study some reduced free products of C*-algebras with amalgamations. We give sufficient conditions for the positive cone of the K_0 group to be the largest possible. We also give sufficient conditions for simplicity and uniqueness of trace. We use the later result to give a necessary and sufficient condition for simplicity and uniqueness of trace of the reduced C*-algebras of the Baumslag-Solitar groups BS(m,n).